Trouble to apply for both Canada green card and USA green card?

Hi,

Landing Canada denied because just got a 2-month new baby but didnot report to visa office. This is not a biggest issue for me.

The worst thing is, I came back to USA with Advance Parole which means I am also in USA immigration process(started 4 years ago, still waiting) --but it is not USA green card yet. The stupid Canada immgration office warned me that double immigration application could hurt both of my applocations in Canada and USA, she told me US immigration will contact me about why did you apply for both?.

If so, application for Canada green card is not backup but a trap?

Highly appreciate,

A man in big trouble waiting for your help!!!